Question

If tan(thetha1+thetha2)=✓3 and sec (thetha1-thetha2)=2/✓3 then sin 2(thetha1)+tan 3(thetha2) is equal to? Answer as soon as possible I'll mark u as brainliest

Answer 1

Note:

thetha 1 = α

thetha 2 = β

tan (α + β) = √3

tan 60° = √3

      (α + β) = 60°      .... 1

sec (α - β) = 2/√3

sec 30° = 2/√3

      (α - β) = 30°      .... 2

On adding 1 and 2,

         (α + β) = 60°

         (α - β) = 30°

         2α = 90°

     ⇒ α = 45°

     ⇒ β = 15°

sin 2α + tan 3β =  sin 90° + tan 45°

                         ⇒ 1 + 1 = 2